Let F(x,y) = (3x +4xy)i + (2x² -y³j

Q: Let f(x, y) = 12x² + 7y² + 3x + 3y+ 6 Find D = frz · fy – fåy-

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Q: Find DF of fcxiy)=x²e° at the point (-2,0)-

A: Given function is fx,y=x2ey. We have to find the ∇f at the point -2,0. We know that ∇f=∂f∂xi+∂f∂yj…

Q: 2. F(x, у) %3D — (у i-2x) y2

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 2x –1 1 , show that y"+ y' + xy +1 c) If y =-

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Q: compute ∫_∂D(x^2ydx+xy^2dy, where D is described by 0≤x≤1, 0≤y≤x

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Q: Let f (x, y) = 2x3 + x2y - y2. Compute d2f/dx2, d2f/dy2, and d2f/dxdy at (x, y) = (1, 2).

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Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: Find and classify the critical points of f(x, y) = 6xy – 4x³ – 3y?

A: According to our guidelines, we can answer only one question or three subparts of a question. other…

Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = 2x3 + 3y2 + 1.

A: To verify that

Q: Evaluate fSS 6e(²+y²+z²)/² dV over B where B= {(x, y, 2) : x² + y² + z² < 1}. Take T = 3.

A: Since we have    x2 + y2 + z2  expression in the integral and region B is the sphere of radius 1…

Q: (b) Integrate f(x, y) = 4e0.8x - 0.5y using h = 0.5 with y(0) 2 from x = 0 to 0.5.

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Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y+ ++ 4y – x16

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Q: find ∇f at the given point. ƒ(x, y, z) = (x2 + y2 + z2)^(-1/2) + ln (xyz), (-1, 2, -2)

A: Given function is  Firstly, we find all first order partial derivatives of f

Q: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

Q: Let f (x,y) =In Then f „(1, – 1) =... 3x²+ 4y3

A: This is a problem of partial.

Q: Find the ditterential of the function y = (x + 1(5x - 3). Sx-x-5 dy = (Sx - 3) *?+ 6x-5 (5x- 3)? dy…

A: Use the quotient rule of differentiation ddxuv=vdudx-udvdxv2. Power rule of differentiation…

Q: Let f (x, y) = x³ + y? – 4xy + 3x + 2y + 5. Find and classify all critical points of f.

A: *concept:- maxima and minima in partial derivatives.

Q: Find the orthogonal trajectories of x² + y² – 2cy = 0

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Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous…

Q: 7. Let f(x, y) = 10x³y* + 21xy². Find fyyy. .3,4

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Q: Suppose that f(x, y, z) = (1+x + y² + z³)4 + ln (1 + 3x + 2y + z).

A: In this question, we approximate the function by using a linear approximation of f(x,y,z)

Q: Integrate f(x, y) = y(x² + y³) 3 over the domain x² + y° 0.

A: Given function is fx,y=yx2+y23 and domain is x2+y2≤4 with y≥0 We have to integrate fx,y=yx2+y23 over…

Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* – 6x – 2y + 1

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Q: Find f, (x.y) if f(x.y)=x - 5xy- 4y2.

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Q: Find f2, fy, and f.- f(x, Y, z) = (4x² + 6y² + 3z²)¯05 fz = fy = f. =

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Q: x, prove that y¨= 2(y² +1)(3y² +1).

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Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y* + + 4y – x16

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Q: Let_y=x² +5x³-4x+1 then dy- ||

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Q: Find (x, y): R = {(x, y): 0 ≤ y ≤ √√x² +1,0 ≤ x ≤ 1} about the x-axis.

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Q: Let f(x,y) = 10x^3y^4+ 21xy^2 Find ?yyy

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Q: Find the linearization of y=2^x at a=0

A: use derivative to find the Linearization of y

Q: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

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Q: Find the orthogonal trajectories of the family of x² – y? = cx = CX -

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Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

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Q: Find the linearization L(x) of y = (64+3x2)-1/2 at a = 0. L(x) = %3D

A: The given function is: y=f(x)=(64+3x2)-12 So, f'(x)=-1264+3x2-32(6x)        =-3x64+3x232

Q: F(x,y) = -41² - 2xy-4y² +z+y.

A: Follow the procedure given below.

Q: What is dufferential equation of x'=4x-y and y'=-4x+4y when t=0, x(0)=1 and y(0)=1

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Q: 1. Find and classify the critical points of f (x, y) = 6xy – 4x³ – 3y?

A: Critical points of f will occur: fx and fy is o. Given equation is f(x,y) = 6xy-4x3-3y2…

Q: Find the linearization L(x) of y=e10xln(x) at a=1

A: y=e10xln(x)  The linearization L(x) of a function f(x) at x = a is, Now  Now differentiating given…

Q: Let f(x,y) = 5x² + 6y² + 3xy – 5x – 8y + 36 What is the first coordinate of the critical point?

A: Given data:   The given expression of the function is f(x,y)=5x2+6y2+3xy-5x-8y+36.     Equate the…

Q: Given f (x,y) = 3 – 2x² – 2xy – 2y² – 16x, find and classify all critical points of f. -

A: Calculate fx, fy , fxx , fyy , fxy for f(x,y)=3-2x2-2xy-2y2-16x as follows.…

Q: Find f(3,4) for f (x, y) = ln(x + Vx² + y²).

A: We have to find out the derivative

Q: Find f (1, 1) S(x, y) = In( %3D Vx² + y²

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Q: Evaluate S. (x – y)dx + xydx where C is the y = 2x2 – 1 from the point (-1,1) to the point (2,7).

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.